Structure of optimal policies in quantum control

TL;DR

This paper uses the Pontryagin maximum principle to analyze the structure of optimal quantum control policies, revealing that most are constrained by technical bounds and only a few are bang-bang, challenging existing conjectures.

Contribution

It provides a generic analysis of optimal policies in quantum control, including the first study of periodic optimization and refuting common conjectures about control structures.

Findings

Most optimal policies are constrained by technical bounds.

Bang-bang controls occur only in specific cases like environmental control.

The results challenge existing beliefs about the structure of optimal quantum controls.

Abstract

Using the Pontryagin maximum principle, the generic structure of optimal policies is deduced for typical quantum control tasks involving coherent lasers, magnetic fields and reservoir engineering. In addition, the periodic optimization is considered for the first time in view of prospective applications. We proved that nearly all optimal policies are actively constrained by technical bounds on control parameter but reduce to entirely bang-bang sequences only in special cases, such as the environmental control by random collisions. The results allow to arguably refute two generally accepted and concurring conjectures regarding the structure of optimal controls.